Giant Spin Splitting through Surface Alloying

Abstract

The long-range ordered surface alloy Bi=Ag 111 is found to exhibit a giant spin splitting of its surface electronic structure due to spin-orbit coupling, as is determined by angle-resolved photoelectron spectroscopy. First-principles electronic structure calculations fully confirm the experimental findings. The effect is brought about by a strong in-plane gradient of the crystal potential in the surface layer, in interplay with the structural asymmetry due to the surface-potential barrier. As a result, the spin polarization of the surface states is considerably rotated out of the surface plane. DOI: 10.1103/PhysRevLett.98.186807 PACS numbers: 73.20.At, 71.70.Ej, 79.60.ÿi In nonmagnetic solids, electronic states of opposite spin orientation are often implicitly taken to be degenerate (Kramers' degeneracy). However, spin degeneracy is a consequence of both time-reversal and inversion symmetry. If one of the latter is broken, the degeneracy can be lifted by, e.g., the spin-orbit (SO) interaction. This is, for example, the case in crystals that lack a center of inversion in the bulk (Dresselhaus effect) [1,2]. But also a structural inversion asymmetry, as it shows up at surfaces or interfaces, can lead to spin-split electronic states [RashbaBychkov (RB) effect] [3]. In particular, clean surfaces of noble metals show spin-split surface states, where the splitting increases with the strength of the atomic SO coupling (cf. Ag and Au in Table I). The splitting can be further enhanced by adsorption of adatoms [9][10][11][12]. Hence, using morphology and chemistry to tune the spin splitting of twodimensional electronic states is a promising path to create a new class of nanoscale structures suitable for spintronic devices. Doping GaAs by only a few percent with Bi atoms has been shown to strongly increase the spin-orbit splitting energy 0 [13]. However, a value for the Rashba-Bychkov type spin splitting has not been reported.The Au(111) L-gap surface state is the paradigm of a Rashba-Bychkov system with a spin splitting of a few tens of meV, that was investigated in detail by means of spinand angle-resolved photoelectron spectroscopy (ARPES) [14]. The nonrelativistic Hamilton operator of the spinorbit interaction,can be expressed for a two-dimensional gas of free electrons (in the xy plane) asin which the Rashba parameter R is essentially determined by the gradient of the potential V in z direction,and is the vector of Pauli matrices. This model reproduces remarkably well the very characteristic dispersion of the spin-split surface-state bands of Au(111). The spin polarizations P of the split and completely polarized (jPj 100%) electronic states lie axially symmetric within the surface plane (P ? k k ? e z ). Time-reversal symmetry requires P k k ÿP ÿk k and E k k E ÿk k . The two main contributions to the spin splitting are a strong atomic SO interaction and a potential gradient along the surface normal (z direction). By adsorption of noble gases and oxygen, the spin splitting was successfully enhanced by increasing ...

Broken symmetry induced band splitting in theAg2Gesurface alloy on Ag(111)

“…However, as reported in that study, the Ge/Ag surface alloy shows an unexpected surface band split at theM points along the¯ KM line of the Ý3 × Ý3 surface Brillouin zone (SBZ). The observation of split bands at theM points clearly indicates that the Ge/Ag alloy differs substantially from the other group IV alloys (Pb/Ag [11] and Sn/Ag [3]; as well as from the alloys induced by Bi [2] or Sb [12]). As was concluded in Ref.…”

“…All of these show a (Ý3 × Ý3)R30°structure where ⅓ monolayer (ML) of the Ag surface atoms is replaced by an M element. In the case of Bi, a giant RB split was reported in the surface band structure of the 2D alloy [2]. The RB split is expected to decrease with decreasing atomic number, and in the case of Sn, no split could be observed [3].…”

Relativistic effects and fully spin-polarized Fermi surface at the Tl/Si(111) surface

“…13,14 On one hand, these types of surfaces have been recently found to exhibit exceptional relativistic effects, 15,16 inducing spin-orbit energy shifts two orders of magnitude bigger than those found at normal semiconductor heterojunctions. From the practical point of view, heavy elements such as Tl or Sb are widely used in electronic instruments such as infrared detectors 17 or Halleffect devices.…”

Formation of Ideal Rashba States on Layered Semiconductor Surfaces Steered by Strain Engineering

“…Noble metal (e.g., Au 6 , Ag 7 , and Ir 8 ) and sp-orbit heavy-metal surfaces (e.g., Bi 9 , Sb 10 and Pb 11 ) were shown to have large spin splitting. Heavy metal adatoms alloying with metal (e.g., Bi/Ag(111) 12 ) and/or semiconductor surfaces (e.g., Bi/Si(111) 13 ) were found to possess giant spin splitting. Most recently, new surface systems with Rashba states have been reported in graphene/Ni(111) 14 and molecule-adsorbed topological insulators [15][16][17] .…”